the most important thing is to be gentle to your skin. Do not use ordinary soap to clean your face since it dehydrates your skin. Best would be a soap free emulsion which is ph-neutral to the skin. Do not fall for advertisement and anti-pimple products. Most of them are way to agressive + useless for a cleansing product should clean and nothing more.

I find it very helpful to let my skin dry through after washing it before i apply a moisturizer. The skin absorbs the moisturizer much better this way.

I recommend you to get some jojoba-oil. You can add some drops to your moisturizer or simply apply a little amount to your skin. Jojoba is the only oil which does not clogg your pores. It sounds weird, but my skin is way less oily since I use jojoba.

Just take care not to irritate your skin. That means you can not wash it more than twice a day.